I would like to know why people are interested in transverse slices. In particular, I would like to know why people study the Slodowy slice to orbits in the nilpotent cone. In Chri …

My question is about an isomorphism between two varieties of the form discussed in this thread; it is also related to an earlier question of mine. Let $z_n$ be the standard nilpot …

I recently learned that there is a natural identification, given a simple Lie algebra, Polynomial functions on the Slodowy slice of a regular nilpotent orbit $\simeq$ polynomi …

Let $G$ be your favorite simple complex Lie group, and $P\subset G$ your favorite parabolic subgroup. We can identify $T^*G/P$ with the space of pairs $$\{(gP,x)\in G/P\times \mat …